Problem: Solve for $r$. $4r-3=3(3r+4)$ $r =$
We need to manipulate the equation to get $ r $ by itself. $\begin{aligned} 4r-3 &= 3(3r+4) \\\\ 4r-3 &= 9r+12~~~~~~~~~~\gray{\text{Distribute}}\\\\ 4r-3{-9r} &= 9r+12{-9r} ~~~~~~~~~~\gray{\text{Subtract 9r from each side}}\\\\ -5r-3&=12 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ -5r-3{+3} &=12 {+3} ~~~~~~~~~~\gray{\text{Add 3 to each side}}\\\\ -5r &= 15~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{-5r}{{-5}}&= \dfrac{15}{{-5}}~~~~~~~~~~\gray{\text{Divide each side by -5}} \\\\ r &= {-3} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ r =-3 { }~~~~~~~~$ [Let's check our work!]